US 6972764 B1 Abstract The preferred method transforms a set of closed curves, such as a typeface, font, or character. The method projects a pattern of continuous curves over the closed curves (502). The method then determines a set of intersection points of the closed curves and continuous curves (506). Cross-over points are then determined from the set of intersection points (508). Closed loops are then assembled from the cross-over points to form the transformed typeface, font or character (510).
Claims(57) 1. A computer-implemented method for generating a graphical object comprising a plurality of closed loops, the method comprising the steps of:
a first providing step of providing a set of one or more closed first curves defining a boundary of a surface, wherein the set of one or more closed first curves contains no self-crossover points;
a second providing step of providing a set of continuous second curves lying on the surface, wherein each of the continuous second curves intersects and crosses over one or more of the closed first curves but does not intersect other ones of the continuous second curves and wherein the set of continuous second curves contains no self-crossover points;
a first determining step in which the computer determines a set of intersection points, wherein the intersection points are those points where the one or more closed first curves intersect the continuous second curves and which lie on the boundary of the surface;
a second determining step in which the computer determines a set of crossover points from the determined set of intersection points;
an assembling step in which the computer assembles, without user intervention, the plurality of closed loops from curve intervals, delimited by adjacent determined crossover points, from the set of one or more closed first curves and the set of continuous second curves in accordance with a predetermined rule, whereby the plurality of closed loops abuts a substantial portion of the boundary of the surface and whereby each of the plurality of closed loops does not share a curve interval with any other one of the closed loops; and
a filling step in which the computer fills the plurality of closed loops with a fill to produce the graphical object.
2. A method as claimed in
an ordering substep of ordering the set of crossover points in accordance with a predetermined order;
a first marking substep of marking one of the crossover points that is highest in the predetermined order and that has not been previously marked;
a determining substep of determining if a last marked crossover point is a first point in a closed loop, and if so performing:
a first selecting substep of selecting a curve interval starting at the first point and terminating at an unmarked crossover point; and
a second marking substep of marking the terminating crossover point of the selected curve interval; or if not performing:
a second selecting substep of selecting a curve interval starting at the previous terminating crossover point and terminating at an unmarked crossover point; and
a third marking substep of marking the current terminating crossover point of the selected curve interval;
a first repetition substep of repetitively performing the determining substep until the closed loop is formed; and
a second repetition substep of repetitively performing the first marking, determining and the first repetition substeps until all possible closed loops have been formed.
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18. An apparatus for generating a graphical object comprising a plurality of closed loops, the apparatus comprising:
first providing means for providing a set of one or more closed first curves defining a boundary of a surface, wherein the set of one or more closed first curves contains no self-crossover points;
second providing means for providing a set of continuous second curves lying on the surface, wherein each of the continuous second curves intersects and crosses over one or more of the closed first curves but does not intersect other ones of the continuous second curves and wherein the set of continuous second curves contains no self-crossover points;
first determining means for determining a set of intersection points, wherein the intersection points are those points where the one or more closed first curves intersect the continuous second curves and which lie on the boundary of the surface;
second determining means for determining a set of crossover points from the set of intersection points;
assembling means for assembling, without user intervention, the plurality of closed loops from curve intervals, delimited by adjacent determined crossover points, from the set of one or more closed first curves and the set of continuous second curves in accordance with a predetermined rule, whereby the plurality of closed loops abuts a substantial portion of the boundary of the surface and whereby each of the plurality of closed loops does not share a curve interval with any ther one of the closed loops; and
filling means for filling the plurality of closed loops with a fill to produce the graphical object.
19. An apparatus as claimed in
ordering means for ordering the set of crossover points in accordance with a predetermined order;
first marking means for marking one of the crossover points that is highest in the predetermined order and that has not been previously marked;
first selecting means for selecting a curve interval starting at a first point and terminating at an unmarked crossover point;
second marking means for marking the terminating crossover point of the selected curve interval;
second selecting means for selecting a curve interval starting at the previous terminating crossover point and terminating at an unmarked crossover point;
third marking means for marking the current terminating crossover point of the selected curve interval;
third determining means for determining if a last marked crossover point is the first point in a closed loop, and if so performing the operations of said first selecting means and said second marking means, or if not, performing the operations of said second selecting means and said third marking means;
means for repetitively performing the operations of said third determining means until the closed loop is formed; and
means for repetitively performing the operations of said first marking means and said third determining means until all possible closed loops have been formed.
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35. A computer program product comprising a computer readable medium including a computer program for generating a graphical object comprising a plurality of closed loops, the computer program product comprising:
first providing means for providing a set of one or more closed first curves defining a boundary of a surface, wherein the set of one or more closed first curves contains no self-crossover points;
second providing means for providing a set of continuous second curves lying on the surface, wherein each of the continuous second curves intersects and crosses over one or more of the closed first curves but does not intersect other ones of the continuous second curves and wherein the set of continuous second curves contains no self-crossover points;
first determining means for determining a set of intersection points, wherein the intersection points are those points where the one or more closed first curves intersect the continuous second curves and which lie on the boundary of the surface;
second determining means for determining a set of crossover points from the set of intersection points;
assembling means for assembling, without user intervention, the plurality of closed loops from curve intervals, delimited by adjacent determined crossover points, from the set of one or more closed first curves and the set of continuous second curves in accordance with a predetermined rule, whereby the plurality of closed loops abuts a substantial portion of the boundary of the surface and whereby each of the plurality of closed loops does not share a curve interval with any other one of the closed loops; and
filling means for filling the plurality of closed loops with a fill to produce the graphical object.
36. A computer program product as claimed in
ordering means for ordering the set of crossover points in accordance with a predetermined order;
first marking means for marking one of the crossover points that is highest in the predetermined order and that has not been previously marked;
first selecting means for selecting a curve interval starting at a first point and terminating at an unmarked crossover point;
second marking means for marking the terminating crossover point of the selected curve interval;
second selecting means for selecting a curve interval starting at the previous terminating crossover point and terminating at an unmarked crossover point;
third marking means for marking the current terminating crossover point;
third determining means for determining if the last marked crossover point is the first point in a closed loop, and if so performing the operations of said first selecting means and said second marking means, or if not, performing the operations of said second selecting means and said third marking means;
means for repetitively performing the operations of said third determining means until the closed loop is formed; and
means for repetitively performing the operations of said first marking means and said third determining means until all possible closed loops have been formed.
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52. A computer-implemented method of modifying a typeface, font, or character, the method comprising the steps of:
a first providing step of providing a set of one or more closed first curves defining a boundary of a surface of the typeface, font, or character, wherein the set of one or more closed first curves contains no self-crossover points;
a second providing step of providing a set of continuous second curves lying on the surface, wherein each of the continuous second curves intersects and crosses over one or more of the closed first curves but does not intersect other ones of the continuous second curves and wherein the set of continuous second curves contains no self-crossover points;
a first determining step in which the computer determines a set of intersection points, wherein the intersection points are those points where the one or more closed first curves intersect the continuous second curves and which lie on the boundary of the surface;
a second determining step in which the computer determines a set of crossover points from the determined set of intersection points;
an assembling step in which the computer, without user intervention, assembles a plurality of closed loops from curve intervals, delimited by adjacent determined crossover points, from the set of one or more closed first curves and the set of continuous second curves in accordance with a predetermined rule, whereby the plurality of closed loops abuts a substantial portion of the boundary of the surface and whereby each of the plurality of closed loops does not share a curve internal with any other one of the closed loops; and
a filling step of filling the plurality of closed loops with a fill to form the modified typeface, font, or character.
53. An apparatus for modifying a typeface, font, or character, the apparatus comprising:
first providing means for providing a set of one or more closed first curves defining a boundary of a surface of the typeface, font, or character, wherein the set of one or more closed first curves contains no self-crossover points;
second providing means for providing a set of continuous second curves lying on the surface, wherein each of the continuous second curves intersects and crosses over one or more of the closed first curves but does not intersect other ones of the continuous second curves and wherein the set of continuous second curves contains no self-crossover points;
means for determining a set of intersection points, wherein the intersection points are those points where the one or more closed first curves intersect the continuous second curves and which lie on the boundary of the surface;
means for determining a set of crossover points from the set of intersection points;
assembling means for assembling, without user intervention, a plurality of closed loops from curve intervals, delimited by adjacent determined crossover points, from the set of one or more closed first curves and the set of continuous second curves in accordance with a predetermined rule, whereby the plurality of closed loops abuts a substantial portion of the boundary of the surface and whereby each of the plurality of closed loops does not share a curve interval with any other one of the closed loops; and
filling means for filling the plurality of closed loops with a fill to form the modified typeface, font, or character.
54. A computer program product comprising a computer readable medium including a computer program for modifying a typeface, font, or character, the computer program product comprising:
first providing means for providing a set of one or more closed first curves defining a boundary of a surface of the typeface, font, or character, wherein the set of one or more closed first curves contains no self-crossover points;
second providing means for providing a set of continuous second curves lying on the surface, wherein each of the continuous second curves intersects and crosses over one or more of the closed first curves but does not intersect other ones of the continuous second curves and wherein the set of continuous second curves contains no self-crossover points;
means for determining a set of intersection points, wherein the intersection points are those points where the one or more closed first curves intersect the continuous second curves and which lie on the boundary of the surface;
means for determining a set of crossover points from the set of intersection points;
assembling means for assembling, without user intervention, a plurality of closed loops from curve intervals, delimited by adjacent determined crossover points, from the set of one or more closed first curves and the set of continuous second curves in accordance with a predetermined rule, whereby the plurality of closed loops abuts a substantial portion of the boundary of the surface and whereby each of the plurality of closed loops does not share a curve interval with any other one of the closed loops; and
filling means for filling the plurality of closed loops with a fill to form the modified typeface, font, or character.
55. A method of modifying a typeface, font, or character, the method comprising the computer-implemented steps of:
receiving a selection from a user of a set of one or more closed first curves defining a boundary of a surface of the typeface, font, or character, wherein the set of one or more closed first curves contains no self-crossover points;
receiving a selection from the user of a set of continuous second curves lying on the surface, wherein each of the continuous second curves intersects and crosses over one or more of the closed first curves but does not intersect other ones of the continuous second curves and wherein the set of continuous second curves contains no self-crossover points;
determining a set of intersection points, wherein the intersection points are those points where the one or more closed first curves intersect the continuous second curves and which lie on the boundary of the surface;
determining a set of crossover points from the set of intersection points;
selecting unmarked adjacent crossover points from the set of determined crossover points to a form a closed loop;
marking the selected adjacent crossover points;
repetitively performing the selecting and marking steps, without intervention from the user, until a set of closed loops have been formed, wherein the set of closed loops abuts a substantial portion of the boundary of the surface; and
filling the set of closed loops with a fill to form the modified typeface, font, or character.
56. Apparatus for modifying a typeface, font, or character, the apparatus comprising:
means for receiving a selection of a set of one or more closed first curves defining a boundary of a surface of the typeface, font, or character, wherein the set of one or more closed first curves contains no self-crossover points;
means for receiving a selection of a set of continuous second curves lying on the surface, wherein each of the continuous second curves intersects and crosses over one or more of the closed first curves but does not intersect other ones of the continuous second curves and wherein the set of continuous second curves contains no self-crossover points;
means for determining a set of intersection points, wherein the intersection points are those points where the one or more closed first curves intersect the continuous second curves and which lie on the boundary of the surface;
means for determining a set of crossover points from the set of intersection points;
means for selecting unmarked adjacent crossover points from the set of determined crossover points to a form a closed loop;
means for marking the selected adjacent crossover points;
means for repetitively performing the operations of said selection means and said marking means, without user intervention, until a set of closed loops have been formed, wherein the set of closed loops abuts a substantial portion of the boundary of the surface; and
means for filling the set of closed loops with a fill to form the modified typeface, font, or character.
57. A computer program product comprising a computer readable medium including a computer program for modifying a typeface, font, or character, the computer program product comprising:
means for receiving a selection of a set of one or more closed first curves defining a boundary of a surface of the typeface, font, or character, wherein the set of one or more closed first curves contains no self-crossover points;
means for receiving a selection of a set of continuous second curves lying on the surface, wherein each of the continuous second curves intersects and crosses over one or more of the closed first curves but does not intersect other ones of the continuous second curves and wherein the set of continuous second curves contains no self-crossover points;
means for determining a set of intersection points, wherein the intersection points are those points where the one or more closed first curves intersect the continuous second curves and which lie on the boundary of the surface;
means for determining a set of crossover points from the set of intersection points;
means for selecting unmarked adjacent crossover points from the set of determined crossover points to form a closed loop;
means for marking the selected adjacent crossover points;
means for repetitively performing the operations of said selection means and said marking means, without user intervention, until a set of closed loops have been formed, wherein the set of closed loops abuts a substantial portion of the boundary of the surface; and
means for filling the set of closed loops with a fill to form the modified typeface, font, or character.
Description The present invention relates to a method and apparatus for transforming a set of closed curves. The invention also relates to a computer program product comprising a computer readable medium including a computer program for transforming a set of closed curves. In the fields of computational geometry and graphics, it is often desirable to modify the shape of an object in some consistent, reproducible and controllable manner, to produce a result that satisfies some criteria regarding shape or form. Such criteria might include the transformation of shapes to those that are considered to be more artistically appealing or complex, but still retain the basic shape of the original outline. For instance, it may be desirable to transform a computer typeface or font defined by character shape outlines to produce more interesting and artistically pleasing results, where the basic overall outline shapes are maintained so that readability is not lost. The publication U.S. Pat. No. 5,701,404 discloses a method for trimming non-uniform rational B-spline surfaces according to curves projected onto them. However, this method suffers from the disadvantage that the basic overall shape of the original outline is not always retained. It is an object of the present invention to ameliorate one or more disadvantages of the prior art. According to one aspect of the invention there is provided a method for transforming a set of closed first curves defined on a surface, wherein the first curves contain no self-crossover points, the method comprising the steps of: (i) providing a pattern comprising a set of continuous second curves for projection over the set of first curves upon the surface, wherein the second curves contain no self-crossover points; (ii) determining a set of intersection points of the set of first curves with the set of second curves; (iii) determining a set of crossover points within the set of intersection points; and (iv) selecting curve intervals, delimited by the crossover points, from the set of first curves and the set of second curves in accordance with a predetermined rule to form closed loops; wherein the closed loops form said transformed set of closed curves. According to another aspect of the invention there is provided apparatus for transforming a set of closed first curves defined on a surface, wherein the first curves contain no self-crossover points, the apparatus comprising; providing means for providing a pattern comprising a set of continuous second curves for projection over the set of first curves upon the surface, wherein the second curves contain no self-crossover points; a first determining means for determining a set of intersection points of the set of first curves with the set of second curves; a second determining means for determining a set of crossover points within the set of intersection points; and a first selecting means for selecting curve intervals, delimited by the crossover points, from the set of first curves and the set of second curves in accordance with a predetermined rule to form closed loops; wherein the closed loops form said transformed set of closed curves. According to still another aspect of the invention there is provided a computer program product comprising a computer readable medium including a computer program for transforming a set of closed first curves defined on a surface, wherein the first curves contain no self-crossover points, the the computer program product comprising; providing means for providing a pattern comprising a set of continuous second curves for projection over the set of first curves upon the surface, wherein the second curves contain no self-crossover points; a first determining means for determining a set of intersection points of the set of first curves with the set of second curves; a second determining means for determining a set of crossover points within the set of intersection points; and a first selecting means for selecting curve intervals, delimited by the crossover points, from the set of first curves and the set of second curves in accordance with a predetermined rule to form closed loops; wherein the closed loops form said transformed set of closed curves. According to another aspect of the present invention there is provided a method of modifying a typeface, font, or character, wherein said typeface, font, or character comprises a set of closed first curves, wherein the set of first curves contain no self-crossover points, the method comprises the steps of: projecting a pattern comprising a set of continuous second curves over the set of first curves, wherein the set of first curves contain no self-crossover points; determining a set of intersection points of the set of first curves with the set of second curves; determining a set of crossover points within the set of intersection points; and selecting curve intervals, delimited by crossover points, from the set of first curves and the set of second curves to form a set of closed third curves, wherein said set of closed third curves form a modified said typeface, font, or character. According to another aspect of the present invention there is provided an apparatus for modifying a typeface, font, or character, wherein said typeface, font, or character comprises a set of closed first curves, wherein the set of first curves contain no self-crossover points, the apparatus comprising: means for projecting a pattern comprising a set of continuous second curves over the set of first curves, wherein the set of first curves contain no self-crossover points; means for determining a set of intersection points of the set of first curves with the set of second curves; means for determining a set of crossover points within the set of intersection points; and means for selecting curve intervals, delimited by crossover points, from the set of first curves and the set of second curves to form a set of closed third curves, wherein said set of closed third curves form a modified said typeface, font, or character. According to another aspect of the present invention there is provided a computer program product comprising a computer readable medium including a computer program for modifying a typeface, font, or character, wherein said typeface, font, or character comprise a set of closed first curves, wherein the set of first curves contain no self-crossover points, the computer program product comprising: means for projecting a pattern comprising a set of continuous second curves over the set of first curves, wherein the set of first curves contain no self-crossover points; means for determining a set of intersection points of the set of first curves with the set of second curves; means for determining a set of crossover points within the set of intersection points; and means for selecting curve intervals, delimited by crossover points, from the set of first curves and the set of second curves to form a set of closed third curves, wherein said set of closed third curves form a modified said typeface, font, or character. According to another aspect of the present invention there is provided a method of modifying a typeface, font, or character, wherein said typeface, font, or character comprises a set of closed first curves, wherein the set of first curves contain no self-crossover points, the method comprises the steps of: projecting a pattern comprising a set of continuous second curves over the set of first curves, wherein the set of first curves contain no self-crossover points; determining a set of intersection points of the set of first curves with the set of second curves; determining a set of crossover points within the set of intersection points; selecting unmarked adjacent crossover points to a form a closed loop; marking the selected adjacent crossover points; and repetitively performing the selecting and marking steps until a set of said closed loops have been formed, wherein said closed loops form a modified typeface, font, or character. According to another aspect of the present invention there is provided an apparatus for modifying a typeface, font, or character, wherein said typeface, font, or character comprises a set of closed first curves, wherein the set of first curves contain no self-crossover points, the apparatus comprising: means for projecting a pattern comprising a set of continuous second curves over the set of first curves, wherein the set of first curves contain no self-crossover points; means for determining a set of intersection points of the set of first curves with the set of second curves; means for determining a set of crossover points within the set of intersection points; means for selecting unmarked adjacent crossover points to a form a closed loop; means for marking the selected adjacent crossover points; and means for repetitively performing the operations of the selection and marking means until a set of said closed loops have been formed, wherein said closed loops form a modified typeface, font, or character. According to another aspect of the present invention there is provided a computer program product comprising a computer readable medium including a computer program for modifying a typeface, font, or character, wherein said typeface, font, or character comprises a set of closed first curves, wherein the set of first curves contain no self-crossover points, the computer program comprising: means for projecting a pattern comprising a set of continuous second curves over the set of first curves, wherein the set of first curves contain no self-crossover points; means for determining a set of intersection points of the set of first curves with the set of second curves; means for determining a set of crossover points within the set of intersection points; means for selecting unmarked adjacent crossover points to a form a closed loop; means for marking the selected adjacent crossover points; and means for repetitively performing the operations of the selection and marking means until a set of said closed loops have been formed, wherein said closed loops form a modified typeface, font, or character. Embodiments of the invention are described with reference to the drawings, in which: Some portions of the detailed descriptions which follow are explicitly or implicitly presented in terms of algorithms and symbolic representations of operations on data within a computer memory. These algorithmic descriptions and representations are the means used by those skilled in the data processing arts to most effectively convey the substance of their work to others skilled in the art. An algorithm is here, and generally, conceived to be a self-consistent sequence of steps leading to a desired result. The steps are those requiring physical manipulations of physical quantities. Usually, though not necessarily, these quantities take the form of electrical or magnetic signals capable of being stored, transferred, combined, compared, and otherwise manipulated. It has proven convenient at times, principally for reasons of common usage, to refer to these signals as bits, values, elements, symbols, characters, terms, numbers, or the like. It should be borne in mind, however, that all of these and similar terms, such as fonts, typefaces or characters, are to be associated with the appropriate physical quantities and are merely convenient labels applied to these quantities. Unless specifically stated otherwise as apparent from the following discussions, it is appreciated that throughout the present invention, discussions utilizing terms such as “selecting”, “determining”, “generating”, “providing”, “comparing”, “orientating” or the like, refer to the action and processes of a computer system, or similar electronic computing device, that manipulates and transforms data represented as physical (electronic) quantities within the computer system's registers and memories into other data similarly represented as physical quantities within the computer system memories or registers or other such information storage, transmission or display devices. The present invention also relates to apparatus for performing the operations herein. This apparatus may be specially constructed for the required purposes, or it may comprise a general purpose computer selectively activated or reconfigured by a computer program stored in the computer. The algorithms and displays presented herein are not inherently related to any particular computer or other apparatus. Various general purpose machines may be used with programs in accordance with the teachings herein, or it may prove convenient to construct more specialized apparatus to perform the required method steps. The structure of a conventional general purpose computer will appear from the description below. In addition, the present invention also relates to a computer program product comprising a computer readable medium including a computer program for orientating a space curve. The computer readable medium is taken herein to include any transmission medium for transmitting the computer program between a source and a designation. The transmission medium may include storage devices such as magnetic or optical disks, memory chips, or other storage devices suitable for interfacing with a general purpose computer. The transmission medium may also include a hard-wired medium such as exemplified in the Internet system, or wireless medium such as exemplified in the GSM mobile telephone system. The computer program is not described with reference to any particular programming language and implementation thereof. It will be appreciated that a variety of programming languages and implementations thereof may be used to implement the teachings of the invention as described herein. Before proceeding with a description of the embodiments, a brief review of terminology used hereinafter is provided. This concept is further illustrated in Now turning to In step 500 of the preferred method, the process commences and a set of closed first curves defined on a 2-dimensional planar surface is inputted. Alternatively, the set of closed first curves may be defined on a 3-dimensional surface, where a 3-dimensional effect is desired. In step 502, a pattern including a set of second curves is generated in response to user input 504. In the next step 506, the intersection points of the set of first curves C and the set of second curves P are determined. The intersection step can be performed efficiently through the use of standard computational methods such as local neighborhood search, or ordering curve segments by coordinate and performing scanline traversal. In the next step 508, a set of crossover points X is determined from the set of intersection points. In this step 508, each intersection point is tested for crossover, resulting in the crossover point set X composed of X_{1 } 1106, X_{2 } 1108, X_{3 } 1110 and X_{4 } 1112. As the curve C is continuous, closed, and contains no self-crossovers, and as the curves P are continuous and contain no self-crossovers within the region R of the closed curve C, then the crossover point set X will always contain an even number of crossover points, as any crossover entering R must have a corresponding crossover leaving R. In the next step 510, the transformed curve set C′ 1122 shown in
Curve intervals are directed according to crossover point ordering, and adjacent intervals are joined at crossover points. The complete loop returns to the start point X_{1}, reclosing the transformed curve. This example results in a transformed curve set C′ 1122 with a single closed curve member, however multiple C′ members may as easily be obtained, and there is not necessarily any correspondence between the cardinality of C and the cardinality of C′. In step 512, the transformed closed set of curves are displayed on a monitor and/or printed. Afterwards, the processing terminates at step 514. Turning now to In step 611, the transformed curve set C′ is set to empty and all the crossover points Xn are marked as “unvisited”. In step 612, the set of crossover points is examined in order, and a new transformed curve is started at an “unvisited” crossover point X_{1}, that is highest in the order. This “unvisited” crossover is then marked as “visited”. In decision block 614, a check is made to determine whether or not the crossover point last marked as “visited” is the first crossover point X_{1 }in the current closed loop. If decision block 614 returns false (No), then processing continues at step 622. Otherwise processing continues at step 616. In step 616, the first curve interval of the current loop selected, delimited by crossover points. This selection process 616 selects the curve interval along C that commences at the first crossover point X_{1 }and that proceeds in the forward direction and terminates at the next adjacent unmarked crossover point X_{2}. In the next step 618, the terminating crossover point X_{2 }is marked as “visited”. In the decision block 620, a check is made whether or not a closed loop has been formed. This is determined by checking whether the last mentioned terminating crossover point X_{n }is the same as the first crossover point X_{1}. If the decision block 620 returns true (Yes), then processing continues at step 625. Otherwise processing continues at decision block 614. If decision block 614 returns false, namely when the last marked crossover point is not the first crossover point X_{1 }in the closed loop, then processing continues at step 622. In step 622, the next curve interval in the current loop is selected delimited by crossover points. This selection process 622 selects the curve interval along C or P that commences at the last marked terminating crossover point and terminates at an unmarked adjacent crossover point. This selection process 622 can thus choose the next curve interval from the four curve intervals available. The selection process selects the first interval encountered around the last marked terminating crossover point in the anticlockwise direction. In the next step 624, the unmarked adjacent crossover point of the selected interval is marked as “visited” and the processing continues at decision block 620. If the decision block 620 determines a closed loop has been formed, then the processing continues at step 625. Otherwise the steps 614, 622, 624 and 620 continue until the transformed loop is formed. In step 625, the transformed closed curve is added to the transformed curve set C′. Given that crossover points by definition result in intervals belonging to alternating curve sets (C, P, C, P and so on) around any crossover point X_{n}, then the first interval encountered around X_{2 }in the anticlockwise direction must belong to P. Also, intervals along C will always be followed in the forward direction, however, intervals along P may be followed in either the positive or negative directions. During the first pass of step 622 the interval X_{2}X_{3 }will be selected. The next interval selected by step 622 is interval X_{3}X_{4}. Arriving at X_{4}, the first interval in anticlockwise order belongs to P, and thus the next pass of step 622 selects interval X_{4}X_{1}. As the next crossover point X_{n }is X_{1}, the curve's starting point, a complete loop has been traversed and the curve is closed and added to the transformed curve set C′. Each terminating crossover point X_{n }is marked as “visited” once a curve interval has been selected and processed. In the decision block 626, a check is made whether or not all closed loops have been formed. This is preferably determined by checking whether all the crossover points X_{n }are marked as “visited”. If the decision block 626 returns true (Yes), then processing continues at step 512 and the transformed curve set C′ is complete. Otherwise the processing is returned to step 612. The preferred method has the advantage that it is applicable to general surfaces, and assumes minimal dependency between the source and target curve sets, beyond their existing on the same surface. The transformation may be safely applied to arbitrary outline shapes provided that they have no self-crossovers. Moreover, the transformation process is consistent, reproducible and controlled so that it can be applied to any outline shape, without the need for intervention by the user beyond the setting of certain parameters. The pattern curve set may be defined implicitly, and calculated on demand to fit the region occupied by the source curve set. In addition, the transformed curve set is preferably alternating, in the sense that neighboring closed regions may touch at common points but do not overlap or intersect. Consequently, a regularly spaced pattern set will result in a set of regularly spaced closed curves alternating with regularly spaced vacant areas. This allows artistic effects such as striping, gradient and checkerboard to be applied to outline shapes. The following examples are simply provided for illustrative purposes of the preferred method and other closed curve sets C and patterns P can be employed without departing from the scope and spirit of the invention. Shown in Turning now to Turning now to In the example illustrated in The crossover point X_{3 } 1412 is next examined and is found to be unvisited. A new transformed curve is started at X_{3}, and the interval X_{3}X_{4 }along C is traversed. At X_{4 } 1414 the interval X_{4}X_{3 }along P is chosen, leading back to this transformed curve's starting point and closing the transformed curve 1418 that is added to C′. At this stage X_{1}, X_{2 }and X_{3 }have been examined as candidates for new transformed curves, and X_{1}, X_{2}, X_{3 }and X_{4 }have been visited. X_{4 }is examined next, but is ignored as it has already been visited, and the transformed curve set C′ is complete.
The next unvisited point in the ordered set X is X_{7}, from which a new transformed curve C_{2}′ 1730 is assembled. In this case, the forward interval along C_{2}X_{7}X_{8 }leads to a visited point X_{8}, so the method backtracks to the C_{2 }point immediately prior to X_{7}, which in this case is the crossover point X_{10}. The crossover point X_{10 }is now treated as the starting point for C_{2}′, and the method proceeds as for the usual case. C_{2}′ is assembled in the following order:
Following this all points X have been visited and the transformed curve set C′ is complete. By way of further example, The preferred method is preferably practiced using a conventional general-purpose computer, such as the one shown in The computer system 2100 consists of the computer 2102, a video display 2116, and input devices 2118, 2120. In addition, the computer system 2100 can have any of a number of other output devices including line printers, laser printers, plotters, and other reproduction devices connected to the computer 2102. The computer system 2100 can be connected to one or more other computers via a communication interface using an appropriate communication channel such as a modem communications path, a computer network, or the like. The computer network may include a local area network (LAN), a wide area network (WAN), an Intranet, and/or the Internet The computer 2102 itself consists of a central processing unit(s) (simply referred to as a processor hereinafter) 2104, a memory 2106 which may include random access memory (RAM) and read-only memory (ROM), input/output (IO) interfaces 2108, a video interface 2110, and one or more storage devices generally represented by a block 2112 in The video interface 2110 is connected to the video display 2116 and provides video signals from the computer 2102 for display on the video display 2116. User input to operate the computer 2102 can be provided by one or more input devices. For example, an operator can use the keyboard 2118 and/or a pointing device such as the mouse 2120 to provide input to the computer 2102. The system 2100 is simply provided for illustrative purposes and other configurations can be employed without departing from the scope and spirit of the invention. Exemplary computers on which the embodiment can be practiced include IBM-PC/ATs or compatibles, one of the Macintosh (TM) family of PCs, Sun Sparcstation (TM), or the like. The foregoing is merely exemplary of the types of computers with which the embodiments of the invention may be practiced. Typically, the processes of the embodiments, described hereinafter, are resident as software or a program recorded on a hard disk drive (generally depicted as block 2112 in In some instances, the program may be supplied to the user encoded on a CD-ROM or a floppy disk (both generally depicted by block 2112), or alternatively could be read by the user from the network via a modem device connected to the computer, for example. Still further, the software can also be loaded into the computer system 2100 from other computer readable medium including magnetic tape, a ROM or integrated circuit, a magneto-optical disk, a radio or infra-red transmission channel between the computer and another device, a computer readable card such as a PCMCIA card, and the Internet and Intranets including email transmissions and information recorded on websites and the like. The foregoing is merely exemplary of relevant computer readable mediums. Other computer readable mediums may be practiced without departing from the scope and spirit of the invention. Applications The preferred embodiment has many areas of application and a number of examples follow but are not seen as exhaustive. One application is the use of the preferred embodiment in the generation of different typefaces or fonts. Another application of the preferred embodiment is in the generation of patterns on objects in digital videos for special effects. The foregoing only describes a small number of embodiments of the present invention, however, modifications and/or changes can be made thereto by a person skilled in the art without departing from the scope and spirit of the invention. Patent Citations
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